# Part A: Income Balance Validation

## Correlation Between Residual and Official BOP Income

- Validation sample: N = 5,748, 173 countries
- Corr(residual income_balance, BOP total income): **0.950**
- Corr(residual, primary income only): 0.820
- Corr(residual, secondary income only): 0.660

## Regression Comparison: Z → Income Balance

| Model | Dep Var | N | Countries | R² | ρ |
|-------|---------|---|-----------|----|----|
| M3-orig: Z → income_balance (residual) | income_balance_gdp | 3,907 | 150 | 0.129 | 0.808 |
| M3-bop: Z → BOP income (official) | bop_income_gdp | 4,086 | 160 | 0.017 | 0.912 |
| M3-primary: Z → primary income | primary_income_gdp | 4,086 | 160 | 0.007 | 0.938 |
| M3-secondary: Z → secondary income | secondary_income_gdp | 4,086 | 160 | 0.182 | 0.766 |

## Z Coefficients Across Income Measures

| Variable | Model | Coef | SE | p-value |
|----------|-------|------|----|---------|
| Z_1 | M3-orig: Z → income_balance (residual) | 41.3648*** | 15.4488 | 0.0074 |
| Z_1 | M3-bop: Z → BOP income (official) | -45.3922** | 22.0320 | 0.0394 |
| Z_1 | M3-primary: Z → primary income | -31.1125*** | 11.9315 | 0.0092 |
| Z_1 | M3-secondary: Z → secondary income | 3.9285 | 11.7208 | 0.7375 |
| Z_2 | M3-orig: Z → income_balance (residual) | -6.3992*** | 2.3132 | 0.0057 |
| Z_2 | M3-bop: Z → BOP income (official) | 5.3223 | 3.3041 | 0.1073 |
| Z_2 | M3-primary: Z → primary income | 4.7389*** | 1.7937 | 0.0083 |
| Z_2 | M3-secondary: Z → secondary income | -1.2475 | 1.7490 | 0.4757 |
| Z_3 | M3-orig: Z → income_balance (residual) | 0.2671*** | 0.0941 | 0.0046 |
| Z_3 | M3-bop: Z → BOP income (official) | -0.1807 | 0.1348 | 0.1801 |
| Z_3 | M3-primary: Z → primary income | -0.1876** | 0.0734 | 0.0106 |
| Z_3 | M3-secondary: Z → secondary income | 0.0655 | 0.0710 | 0.3562 |